Teaching Fractions: How To Introduce Fraction Concepts – the elementary math consultant | Math

# Teaching Fractions: How To Introduce Fraction Concepts – the elementary math consultant

MATHEMATIC HISTORY

Mathematics is one of many oldest sciences in human history. In ancient times, Mathematics was defined since the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it’s no more possible to explain it in several sentences. What I’ve to express now is going to be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art like painting and music. The great majority of mathematicians perform it being an art. From this viewpoint, the truth that a work done, a developed theory works in one way or another apart from mathematics does not concern them much. What matters for them is the depth of the task done, the novelty of the methods used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the objective of science is the universe; When it is to know, rule and direct everything in the universe, we should be able to read the book of nature. The book of nature is written in the language of mathematics, with the highly cited words of Galile; its letters are shapes of geometry. In order to understand and interpret them, we must know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also notice it as a game. Mathematics is just a tool for the user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I do not believe those who cope with mathematics are more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The phrase mathematics, for the very first time, BC. It was used by the members of the Pythagorean school in the 550s. His entry to the written literature, with Plato BC. It was in the 380s. The phrase meaning is “what must be learned”, that is, information. In the years before these dates, instead of the word mathematics, words that mean geometry, equivalent to it in geometry or old languages ​​were used.

It is extremely hard to express anything definite about where and how mathematics started. When we take documents which are not based on archaeological findings that want interpretation, but open enough to require interpretation, We can say that it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands are not suited to agriculture; It is the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, by the end of the floods brought on by the Nile river every year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of their state, who are responsible for these works, should come to take the mandatory measurements and give the landowners as much land as they had in the previous year. Herodotus says that geometry has begun to emerge consequently of those measurements and calculations. A second opinion concerning the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was created in Egypt. However it was born out from the boredom of clergymen and priests, not the necessity for measurement-calculation due to Nile floods. During those times, the only real intellectual class of countries such as Egypt was the priest class. Because the livelihood of this class is supplied by the public or their state, they have much time for you to give to intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of the period, in the same way others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests wanted to simplify the job of the geometric, or they learned how to calculate the areas of some geometric shapes such as for instance triangular and trapezoidal to test that the distribution was fair, and this way generated the birth of geometry.

We shall divide the written history of mathematics into five periods. The initial period will be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The next period, BC. 500-M.S. It’ll cover an amount of 1000 years, known as the Greek Mathematics period, between 500 years. The third term, M.S. It’ll cover a 1200-year period from the 500’s until the start of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, called the golden age of mathematics, dating from 1700-1900. The time scale we are surviving in, dating back to early 1900s, called age modern mathematics, will be the fifth period. I will try to provide details about the development of mathematics in that period, contributing mathematicians, the spot of mathematics in social life and the basic options that come with mathematics in that period.

We will start the very first semester with Egyptian mathematics. Written documents about ancient Egyptian mathematics and generally Egyptian history – I don’t mean the remains of archaeological works – are almost nonexistent. There are two major causes for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason may be the 3 big fires of the Alexandria libraries, the final of these fires happened through the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus could be the leaves of a reddish, reed type plant growing in the Nile delta, typically 15-25 meters long and 30-50 inches wide. These leaves were used to write text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the term papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it is flaky as a result of moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to possess been hidden under exceptional circumstances. The key sources of our knowledge of Egyptian mathematics are these two papyri. The initial of these papyrus is just a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is a copy written by a “mathematician” named Ahmes in the 1650s. This papyrus was bought by the Irish antiquarian H. Rhind in the 1850s, now in the British museum. This papyrus is a book written to instruct math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions are given with their solutions. They’re the sort of questions people can encounter in everyday life, such as sharing account, interest calculation, or finding the location of ​​some geometric shapes. This really is more or less our 8th grade mathematics. The second papyrus, called the Moscow papyrus and now in the Moscow museum, is also BC. It is a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the sort of questions in the Ahmes papyrus, except for the two. Are you aware that other two questions, one may be the calculation of the quantity and part of ​​the surface of the sphere part cut by way of a plane. One other may be the question of finding the amount of a pyramid cut with a plane. Both questions were solved correctly. Those two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians realized that the region of ​​the circle was proportional to its diameter and found the number of pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained only at that level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians began to dominate the middle east. B.C. By the 550s, Persians are the sole rulers of the whole middle east, including Anatolia and Egypt. The Persians organize three trips to Greece between 500-480 BC; They captured Athens in 480, but burned it, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 could be the date that was accepted as the beginning of Greek civilization. This date is the beginning of a really bright period in science, art and literature. Greek mathematics actually started sooner than this period. Two people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he went to Egypt, stayed there for a time and learned geometry in Egypt. Whilst in Egypt, it is described in books where he calculates the height of the fantastic pyramid by measuring along the shadow of the great pyramid, multiplying this number by the ratio of its length to along the current shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to instruct what he learned. It’s assumed that abstract proof based on reasoning, which will be not based on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is recognized as the initial philosopher in human history. He was born on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, went to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up to Babylon by capturing the Persians throughout the occupation of Egypt by the Persians. it’s known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after time for Samos, he created a college and tried to show the folks he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior folks of this school called “mathematics” live together and they’re connected to one another with oath. The second group includes students attending school. Pythagoras school is founded on number cult. According in their mind, everything can be reduced to numbers; It comes with an unusually perfect harmony among numbers, and harmony is a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as for example 1,2,3,…; and kes, ¾,… are the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called the Pythagorean theorem (the square of the proper sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Most of the members of the Pythagorean school were massacred by a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As can be understood from this information, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.